The lunar eclipse is going on right now (not that I can see it ) and I went into Space Engine just to take a quick look at the eclipse there. Much to my surprise, there was no eclipse. In fact, the Moon was nowhere near Earth's shadow. I went into Celestia to see what it had to show, and just as I expected the eclipse was exactly as it should have been.

It seems that the orbit data, at least for Earth and/or the Moon, is somewhat inaccurate in this version of the program. Is this a known issue, and is there any plan to correct this in a future version?

This is a known problem. SpaceEngine handles orbits as Kepler ellipces, but the Moon requires a more accurate analytic trajectory representation. In some of the future versions I'll implement vsop87 numerical model of our Solar system, so the eclipses will be right.